Robust topology optimization of skeletal structures with imperfect structural members
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A topology optimization framework is proposed for robust design of skeletal structures with stochastically imperfect structural members. Imperfections are modeled as uncertain members’ out-of-straightness using curved frame elements in the form of predefined functions with random magnitudes throughout the structure. The stochastic perturbation method is used for propagating the imperfection uncertainty up to the structural response level, and the expected value of performance measure or constraint is used to form the stochastic topology optimization problem. Sensitivities are derived explicitly using the adjoint method and are used in conjunction with an efficient gradient-based optimizer in search for robust optimal topologies. Topological designs for three representative examples are investigated with the proposed algorithm and the resulting topologies are compared with the deterministic designs. It is observed that the new designs primarily feature load path diversification, which is pronounced with increasing level of uncertainty, and occasionally member thickening to mitigate the impact of the uncertainty in members’ out-of-straightness on structural performance.
KeywordsTopology optimization Gradient-based optimizer Adjoint method Structural imperfections Stochastic perturbation Curved beam element
This work was supported by the National Science Foundation under Grant No. CMMI-1401575. This support is gratefully acknowledged. Asadpoure also acknowledges support from University of Massachusetts College of Engineering.
- Cambou B (1975) Application of first-order uncertainty analysis in the finite element method in linear elasticity. In: Proceedings of 2nd international conference on applications of statistics and probability in soil and structural engineering, pp 67–87Google Scholar
- Hisada T, Nakagiri S (1981) Stochastic finite element method developed for structural safety and reliability. In: Proceedings of the 3rd international conference on structural safety and reliability, pp 395–408Google Scholar
- Jansen M, Lombaert G, Schevenels M (2015) Robust topology optimization of structures with imperfect geometry based on geometric nonlinear analysis. Comput Methods Appl Mech Eng 285:452–467. https://doi.org/10.1016/j.cma.2014.11.028, http://www.sciencedirect.com/science/article/pii/S004578251400454X MathSciNetCrossRefGoogle Scholar
- Keshavarzzadeh V, Fernandez F, Tortorelli DA (2017) Topology optimization under uncertainty via non-intrusive polynomial chaos expansion. Comput Methods Appl Mech Eng 318:120–147. https://doi.org/10.1016/j.cma.2017.01.019, http://www.sciencedirect.com/science/article/pii/S0045782516313019 MathSciNetCrossRefGoogle Scholar
- Moens D, Vandepitte D (2005) A survey of non-probabilistic uncertainty treatment in finite element analysis. Comput Methods Appl Mech Eng 194(1216):1527–1555, special Issue on Computational Methods in Stochastic Mechanics and Reliability Analysis. https://doi.org/10.1016/j.cma.2004.03.019 CrossRefGoogle Scholar
- The MathWorks Inc (2017) MATLAB - Optimization Toolbox, Version 7.6. The MathWorks Inc., Natick, Massachusetts, http://www.mathworks.com/products/optimization/